Divide ((k^2-2k)/3)÷((k-2)/k)

$\frac{k^{2} - 2 k}{3} \div \frac{k - 2}{k}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{k^{2} - 2 k}{3} \cdot \frac{k}{k - 2}$

Step 2

Factor $k$ out of $k^{2} - 2 k$ .

Factor $k$ out of $k^{2}$ .

$\frac{k \cdot k - 2 k}{3} \cdot \frac{k}{k - 2}$

Factor $k$ out of $- 2 k$ .

$\frac{k \cdot k + k \cdot - 2}{3} \cdot \frac{k}{k - 2}$

Factor $k$ out of $k \cdot k + k \cdot - 2$ .

$\frac{k (k - 2)}{3} \cdot \frac{k}{k - 2}$

Step 3

Cancel the common factor of $k - 2$ .

Factor $k - 2$ out of $k (k - 2)$ .

$\frac{(k - 2) k}{3} \cdot \frac{k}{k - 2}$

Cancel the common factor.

$\frac{(k - 2) k}{3} \cdot \frac{k}{k - 2}$

Rewrite the expression.

$\frac{k}{3} k$

Step 4

Combine $\frac{k}{3}$ and $k$ .

$\frac{k \cdot k}{3}$

Step 5

Raise $k$ to the power of $1$ .

$\frac{k^{1} k}{3}$

Step 6

Raise $k$ to the power of $1$ .

$\frac{k^{1} k^{1}}{3}$

Step 7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{k^{1 + 1}}{3}$

Step 8

Add $1$ and $1$ .

$\frac{k^{2}}{3}$